The standard tag is fired once when the page loads, so your later changes to the google_tag_params object do not trigger the tag to fire a second time.
If you want to do multiple firings of the remarketing tag without refreshing the entire page then you can try using the asynchronous version of the remarketing tag that allows you to dynamically fire the tag as many times as your like based on user actions on the page.
There are some details about the asynchronous version of the tag here: https://developers.google.com/adwords-remarketing-tag/